Weighted Mean Calculator
The weighted mean (also called the weighted average) is an important statistical measure used when different data points contribute unequally to the average. Unlike the simple mean, where all values are treated equally, the weighted mean assigns a different weight to each value based on its significance or frequency.
What is a Weighted Mean?
The weighted mean is calculated by multiplying each data point by its respective weight and then dividing the sum of these products by the total of the weights. This method helps to give more importance to certain values in a dataset.
Calculator
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| Step | Details |
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Weighted Mean Formula
The formula for calculating the weighted mean is:
Weighted Mean = (Σ (xᵢ * wᵢ)) / Σwᵢ
Where:
- xᵢ is the data value (observation),
- wᵢ is the weight assigned to that value,
- Σ represents the summation over all data points.
How to Use the Weighted Mean Calculator
To use a weighted mean calculator, follow these simple steps:
- Enter each data point into the calculator.
- Assign a weight to each data point based on its importance.
- Click the calculate button to get the weighted mean result.
Example Calculation
Consider a scenario where you have the following data and weights:
| Data Point | Weight |
|---|---|
| 10 | 2 |
| 20 | 3 |
| 30 | 1 |
To calculate the weighted mean:
Weighted Mean = (10 * 2 + 20 * 3 + 30 * 1) / (2 + 3 + 1)
= (20 + 60 + 30) / 6
= 110 / 6
= 18.33
The weighted mean of the dataset is 18.33.
Applications of Weighted Mean
The weighted mean is commonly used in various fields such as:
- Education: To calculate weighted averages for student grades, where different assignments or exams may have different levels of importance.
- Finance: In portfolio analysis, where assets have different amounts invested.
- Economics: For calculating inflation rates or GDP growth rates when different components have varying levels of importance.